Chapter 15 Waves

Question 15.1. Water waves produced by a motor boat sailing in water are

(a) neither longitudinal nor transverse.

(b) both longitudinal and transverse.

(c) only longitudinal.

(d) only transverse.

Question 15.2. Sound waves of wavelength $\lambda$ travelling in a medium with a speed of v m/s enter into another medium where its speed is 2v m/s. Wavelength of sound waves in the second medium is

(a) $\lambda$

(b) $\frac{\lambda}{2}$

(c) $2\lambda$

(d) $4\lambda$

Question 15.3. Speed of sound wave in air

(a) is independent of temperature.

(b) increases with pressure.

(c) increases with increase in humidity.

(d) decreases with increase in humidity.

Question 15.4. Change in temperature of the medium changes

(a) frequency of sound waves.

(b) amplitude of sound waves.

(c) wavelength of sound waves.

(d) loudness of sound waves.

Question 15.5. With propagation of longitudinal waves through a medium, the quantity transmitted is

(a) matter.

(b) energy.

(c) energy and matter.

(d) energy, matter and momentum.

Question 15.6. Which of the following statements are true for wave motion?

(a) Mechanical transverse waves can propagate through all mediums.

(b) Longitudinal waves can propagate through solids only.

(c) Mechanical transverse waves can propagate through solids only.

(d) Longitudinal waves can propagate through vacuum.

Question 15.7. A sound wave is passing through air column in the form of compression and rarefaction. In consecutive compressions and rarefactions,

(a) density remains constant.

(b) Boyle’s law is obeyed.

(c) bulk modulus of air oscillates.

(d) there is no transfer of heat.

Question 15.8. Equation of a plane progressive wave is given by $y = 0.6 \sin 2\pi\left(t - \frac{x}{2}\right)$. On reflection from a denser medium its amplitude becomes 2/3 of the amplitude of the incident wave. The equation of the reflected wave is

(a) $y = 0.6 \sin 2\pi\left(t + \frac{x}{2}\right)$

(b) $y = -0.4 \sin 2\pi\left(t + \frac{x}{2}\right)$

(c) $y = 0.4 \sin 2\pi\left(t + \frac{x}{2}\right)$

(d) $y = -0.4 \sin 2\pi\left(t - \frac{x}{2}\right)$

Question 15.9. A string of mass 2.5 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in

(a) one second

(b) 0.5 second

(c) 2 seconds

(d) data given is insufficient.

Question 15.10. A train whistling at constant frequency is moving towards a station at a constant speed V. The train goes past a stationary observer on the station. The frequency n' of the sound as heard by the observer is plotted as a function of time t (Fig 15.1) . Identify the expected curve.

(a)

(b)

(c)

(d)

Question 15.18. A sonometer wire is vibrating in resonance with a tuning fork. Keeping the tension applied same, the length of the wire is doubled. Under what conditions would the tuning fork still be is resonance with the wire?

Question 15.19. An organ pipe of length L open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of 480 Hz. What should be the length of a pipe closed at one end, so that it also vibrates in its first harmonic with the same tuning fork?

Question 15.20. A tuning fork A, marked 512 Hz, produces 5 beats per second, where sounded with another unmarked tuning fork B. If B is loaded with wax the number of beats is again 5 per second. What is the frequency of the tuning fork B when not loaded?

Question 15.21. The displacement of an elastic wave is given by the function $y = 3 \sin\omega t + 4 \cos\omega t$. where y is in cm and t is in second. Calculate the resultant amplitude.

Question 15.22. A sitar wire is replaced by another wire of same length and material but of three times the earlier radius. If the tension in the wire remains the same, by what factor will the frequency change?

Question 15.23. At what temperatures (in °C) will the speed of sound in air be 3 times its value at O°C?

Question 15.24. When two waves of almost equal frequencies $n_1$ and $n_2$ reach at a point simultaneously, what is the time interval between successive maxima?

Question 15.25. A steel wire has a length of 12 m and a mass of 2.10 kg. What will be the speed of a transverse wave on this wire when a tension of $2.06 \times 10^4$N is applied?

Question 15.26. A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a source of 1237.5 Hz ? (sound velocity in air = 330 m s⁻¹)

Question 15.27. A train standing at the outer signal of a railway station blows a whistle of frequency 400 Hz still air. The train begins to move with a speed of 10 m s⁻¹ towards the platform. What is the frequency of the sound for an observer standing on the platform? (sound velocity in air = 330 m s⁻¹)

Question 15.28. The wave pattern on a stretched string is shown in Fig. 15.2. Interpret what kind of wave this is and find its wavelength.

Question 15.29. The pattern of standing waves formed on a stretched string at two instants of time are shown in Fig. 15.3. The velocity of two waves superimposing to form stationary waves is 360 ms⁻¹ and their frequencies are 256 Hz.

(a) Calculate the time at which the second curve is plotted.

(b) Mark nodes and antinodes on the curve.

(c) Calculate the distance between A' and C'.

Question 15.30. A tuning fork vibrating with a frequency of 512Hz is kept close to the open end of a tube filled with water (Fig. 15.4). The water level in the tube is gradually lowered. When the water level is 17cm below the open end, maximum intensity of sound is heard. If the room temperature is 20°C, calculate

(a) speed of sound in air at room temperature

(b) speed of sound in air at 0°C

(c) if the water in the tube is replaced with mercury, will there be any difference in your observations?

Question 15.31. Show that when a string fixed at its two ends vibrates in 1 loop, 2 loops, 3 loops and 4 loops, the frequencies are in the ratio 1:2:3:4.

Question 15.32. The earth has a radius of 6400 km. The inner core of 1000 km radius is solid. Outside it, there is a region from 1000 km to a radius of 3500 km which is in molten state. Then again from 3500 km to 6400 km the earth is solid. Only longitudinal (P) waves can travel inside a liquid. Assume that the P wave has a speed of 8 km s⁻¹ in solid parts and of 5 km s⁻¹ in liquid parts of the earth. An earthquake occurs at some place close to the surface of the earth. Calculate the time after which it will be recorded in a seismometer at a diametrically opposite point on the earth if wave travels along diameter?

Question 15.33. If c is r.m.s. speed of molecules in a gas and v is the speed of sound waves in the gas, show that c/v is constant and independent of temperature for all diatomic gases.

Question 15.34. Given below are some functions of x and t to represent the displacement of an elastic wave.

(a) $y = 5 \cos(4x) \sin(20t)$

(b) $y = 4 \sin(5x – t/2) + 3 \cos(5x – t/2)$

(c) $y = 10 \cos[(252 – 250)\pi t] \cos[(252+250)\pi t]$

(d) $y = 100 \cos(100\pi t + 0.5x)$

State which of these represent

(a) a travelling wave along –x direction

(b) a stationary wave

(c) beats

(d) a travelling wave along +x direction.

Given reasons for your answers.

Question 15.35. In the given progressive wave

$y = 5 \sin(100\pi t – 0.4\pi x)$

where y and x are in m, t is in s. What is the

(a) amplitude

(b) wave length

(c) frequency

(d) wave velocity

(e) particle velocity amplitude.

Question 15.36. For the harmonic travelling wave $y = 2 \cos 2\pi(10t–0.0080x + 3.5)$ where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of

(a) 4 m

(b) 0.5 m

(c) $\frac{\lambda}{2}$

(d) $\frac{3\lambda}{4}$ (at a given instant of time)

(e) What is the phase difference between the oscillation of a particle located at x = 100cm, at t = T s and t = 5 s?