Waves, Frequency & Amplitude, Summaries of Physics

Download Waves, Frequency & Amplitude and more Summaries Physics in PDF only on Docsity! Unit-3 (Waves) Amplitude: It is defined as the max displacement from the mean position of a transverse wave. It depends on energy. The greater the energy, the greater the amplitude. Wavelength: It is defined as the distance between 2 successive points where they are inphase. It is denoted by λ & its unit is metre. It depends on wave speed. The greater the wave speed, the greater the wavelength. Time period: It is defined as the time taken to complete 1 wave. It is denoted by 'T' & its unit is second. Frequency: It is defined as the no. of waves passing thru a point per unit time. It is denoted by 'f' & its unit is Hertz (Hz) or s⁻¹. It depends on source. If source changes, frequency changes. The relationship between time period & frequency is F = 1 / T . The relationship between speed, frequency & wavelegth are given below: According to the definition of speed, we know: speed = distance / time v = x / t In terms of wave, if x = λ: v = λ / T v = 1 / T × λ v = fλ Following diagram represents, a displacement-time graph for transverse wave: a) State the amplitude for this transverse wave. b) Mark with letter P & Q on this above diagram where the particle is momentarily at rest & has max velocity. c) Describe the motion of the particles in this wave. d) Calculate the time period and hence determine the frequency. e) Calculate if the speed of this wave is 2.5 cm/s. Now calculate the wavelength. f) State and explain what happens to the wavelength of this wave if the speed of this wave is double. Answers: An experiment to investigate speed of water wave using ripple tank experiment: Student A rotates a buzzer emitting fixed frequency of sound. The frequency of sound heard by student A remains same bcoz the distance from the buzzer from student A remains same. Student B hears different frequency of sound. When this buzzer moves towards student B, wavefronts compress & wavelegth decreases. Frequency increases. Speed of sound remains same. When this buzzer moves away from student B, wavefronts stetches, wavelength increases. Frequency of sound decreases. Electromagnetic Wave: The vibration of electric field & magnetic field perpendicular to each other & also perpendicular to the direction of wave motion in a wave is called electromagnetic wave. There are 7 types of electromagnetic wave. According to increase in wavelength, all electromagnetic waves are given below: Radio wave has the longest wavelength & the ray has shortest wavelength. Common properties of all electromagnetic waves are given below: a) They are all transverse wave. b) They can travel thru vacuum. c) They have same speed in vacuum. (3 × 10⁸ m/s) d) They can transfer energy & info. e) They can be reflected & refracted. Gamma ray: It is a high frequency & shortest wavelength of electromagnetic wave. It is emitted from an unstable nucleus & detected by using a G-M Tube. Exposure to gamma radiation can damage healthy cells & lead to cancer. However, gamma rays can also be used to treat cancer. Radiotherapy uses gamma rays to kill cancer cells. It is also used to sterilize medical equipment as it kills bacteria. Properties of image: a) Same size as object. b) Image distance must be equal to the object distance. c) The image is laterally inverted. d) The image is virtual. e) Same color as object. To ensure that the image is at correct position, we have to measure the distance between image & object using ruler. If these 2 distances are same, the image at correct position. The image formed by the plane mirror is virtual bcoz the ray of light does not actually meet at that point where the image is formed. Real image is formed on a cinema screen & projector screen because the ray of light actually meets on these screens. Regular reflection & diffuse reflection: When a beam of light is incident on a flat, smooth surface in a parallel manner, these rays of lights are reflected from this surface in a parallel manner. This reflection is called regular reflection or uniform reflection. When a beam of light is incident on an irregular surface in a parallel manner, these rays of lights are reflected in different directions. This reflections is called diffuse reflection or irregular reflection. Mirror periscope: This periscope is used in a submarine to see the outside from the inside. It consists of 2 mirrors in it as shown below: At first, the ray of light enters the periscope & strikes the first mirror at an angle of 45°. This ray of light is reflected according to law of reflection & strikes the mirror at an angle of 90°. Therefore, the overall ray of light is reflected by 180°. Therefore, an upright image is seen thru the periscope. Refraction of light: Change in direction of light when it passes optically from one medium to another medium due to change in speed of light as well as wavelength is called refraction of light. Construction of ray diagram: 1) From less dense to more dense medium: When any ray of light passes from less dense to more dense medium at an angle due to decrease in speed as well as wavelength but frequency remains same. The ray of light is refracter towards normal. Some of this ray of light is reflected from the boundary between 2 mediums is called partial reflection. Following diagram represents, a mixture of red & violet color is incident on a glass block as shown below: The speed of red & violet color are same in vacuum but when they enter the glass blocl, they have different speed depending on their different wavelengths. The wavelength of red color is greater than that of violet color. So the speed of red color in the glass block is greater than that of violet color according to V = fλ. Therefore, violet color is refracted more towards normal compared to red color. So the refractjve index of glass for violet is greater than that of red according to n = 𝑠𝑖𝑛 i / 𝑠𝑖𝑛 r . This effect is known as dispersion. An experiment to determine the refractive index of glass block: At first, a glass block is placed on a white paper & its boundary is drawn using a pencil. Now, a ray of light is incident on the glass block from a ray box. This light ray is observed from the opposite side of the glass block. Now, these incident & emergent rays are traced using pins. Now, the glass block is removed & the point if incident & emergent are joined using a scale & pencil. Now, a normal is drawn at the point of incident. Incident & refracted angle are measured using a protractor. This process is repeated for different incident angle & corresponding refracted angle is found. In this experiment, incident angle is independent variable & refracted angle is dependent variable. To get a fair test in this experiment, same type of glass block should be used. It is called control variable. If this variable changes, the experiment will not be fair. A graph of 𝑠𝑖𝑛 i against 𝑠𝑖𝑛 r is plotted. The graph should be a straight line through the origin. The gradient of this graph gives refractive index. To improve the accuracy of this experiment: a) Experiment should be repeated for same incident angle & average angle is found. It reduces the effect of random error. b) The incident angle should be taken as large as possible. It reduces the percentage error. c) The ray of light should be taken as thin as possible or the line drawn on the paper should be taken as thin as possible to measure the angle as accurate as possible. d) Single color of light should be used for this investigation to prevent dispersion effect. Safety precautions: a) Wear safety goggles bcoz the light is very intense. It might damage the eyes. Critical angle: When any ray of light passes from more dense to less dense medium, the ray of light is refracted from normal due to increase in speed & wavelength. Frequency remains same. Some of this ray of light is reflected partially & due to this, the intensity of refracted ray is always less than the intenisty of incident ray. The angle of incidence for which the refracted angle is 90° when the ray of lighy passes feom more dense to less dense medium. This incident angle is called critical angle. It is denoted by 'C'. Condition of critical angle: a) Refracted angle will be 90°. b) Ray if lught oasses form more dense to less dense medium. Relationship between refractive index & critical angle: We know, when any ray of light passes from more dense to less dense medium, This is the relationship between refractive index & critical angle. The greater the denser medium, the ray of light is refracted more towards the normal which decreases the refracted angle & increases the refractive index according to n = 𝑠𝑖𝑛 i / 𝑠𝑖𝑛 r . Therefore, critical angle decreases according to n = 1 / 𝑠𝑖𝑛 C . Total internal reflection: When any ray of light passes from more dense to less dense medium at an angle of incidence which is less than critical angle, the ray of light is reflected away from normal. This is called partial reflection. When this incident angle is greater than critical angle, the ray of light is totally internally reflected to more dense medium. This effect is known as total internal reflection. When total internal reflection takes place, the ray of light follows the law of reflection. Conditions of total internal reflection: If ultraviolet radiator passes thru the prism, it is found below the violet color bcox the wavelength of ultraviolet is less than that of visible light. TOPIC: SOUND WAVE Sound is a longitudinal wave bcoz the particles in a medium vibrate back & forth parallel to wave motion, creating a series of compressions & rarefactions. The separation between 2 compressions & rarefactions give the wavelength of sound wave. In a region of compressions, no. of air particles per unit vol is greater. So the air pressure is greater than atmospheric pressure. In a region of rarefactions, no. of air particles per unit vol is less. So air pressure is less than the atmospheric pressure. Following diagram represents, air pressure against distance graph: An experiment to demonstrate that sound cannot travel thru vacuum: Determination of frequency of sound suing C.R.O (Cathode Ray Oscilloscope): Loudspeaker produces a fixed frequency of sound. This sound is received by the microphone. A C.R.O attached to this microphone detects this sound wave as a v-t graph on its screen. By using this v-t graph, we can determine the frequency if sound. At first, we have to count no. of boxes in x direction in the C.R.O screen to complete 1 wave. Then it is multiplied with the time base setting to get the time period. The by using f = 1 / T to calculate the frequency of sound emitted from the loudspeaker. Following diagram represents, v-t graph found on the C.R.O screen: According to this above diagram, time base setting = 10 m/s. Number of square to complete 1 wave: Time period/T = 4 × 10 m/s T = 40 m/s So, T = 40 × 10⁻³ s Therefore, frequency of this sound can be determined by using: f = 1 / T f = 1 / 40 × 10⁻³ f = 25 Hz So, this loudspeaker emittes 25 Hz sound. If this loudspeaker produces higher frequency & higher amplitude of sound, this sound wave takes less no. of squares in x direction to complete 1 wave bcoz time period decreases & the voltage gained in y direction increases. The new shape of the graph is shown in the above diagram using dotted line. An experiment to determine speed of sound in air: At first, 2 persons stand in an open field far away from each other. Person 1 is holding a gun & Person 2 a stopwatch. The separation between these 2 ppl is measured using measuring tape. When Person 1 fires the gun at a time & light & sound are produced. Person 2 starts the stopwatch after seeing light & stops the stopwatch after hearing sound & time taken is recorded. This process is repeated & average time taken is calculated. It reduces the effect of random error. The experiment is again repeated in reverse direction to eliminate the effect of wind speed & average time taken is calculated. Then by using v = x / t, the speed of sound is calculated. To get a fair test in this experiment, temperature, wind speed, air resistance & humidity should be kept constant. These are called control variables. Supersonic speed & sonic bomb: As we go up above the earth surface, no. of air particles per unit vol decreases. We kniw, speed of sound depends on the density of medium. Since the density of air particles decreases with increasing height, so the speed of sound decreases with height.