Waves

When a tuning fork is excited, molecules of air vibrate in accordance with the equation x = A cos(512πt). When this tuning fork and another identical tuning fork loaded with a little wax are excited together, 4 beats are heard. What is the frequency of the second fork loaded with wax.

A person carrying a whistle, emitting continuously a note of frequency 272Hz is running towards a reflecting surface with a speed of 18 km/hr. The speed of sound in air is 345 m/s. The number of beats heard by him per second is

The apparent frequency of the whistle of an engine changes in the ratio 9:8 as the engine passes a stationary observer. If the velocity of the sound is 340 ms^-1, then the velocity of the engine is

Two trains A and B approach a station from opposite sides, sounding their whistles. A stationary observer on the platform hears no beats. If the velocities of A and B are 15 m/s and 30 m/s respectively and the real frequency of the whistle of B is 600 Hz, the real frequency of the whistle of A is (Velocity of sound = 330 m/s)

A wave travelling along a string is described by y(x, t) = 0.005 sin (80.0 x – 3.0 t), in which the numerical constants are in SI units (0.005 m, 80.0 rad m^-1) and  3.0 rad s^-1. 

Calculate 

(a) the amplitude

(b) the wavelength, and 

(c) the period and frequency of the wave

A SONAR system fixed in a submarine operates at a frequency 40.0 kHz. An enemy submarine moves towards the SONAR with a speed of 360 km h^–1. What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be 1450 ms^–1.

Prove that a travelling wave, at an open boundary is reflected without any phase change.

Almost the entire length of an aluminum pipe of length 1.1m is dipped vertically in water contained in a tall jar. An excited tuning fork of frequency 500 Hz is held at the upper end of the pipe and the pipe is gradually raised. How many discrete resonance conditions are possible? (Speed of sound in air = 330 m/s)

Given below are some examples of wave motion. State in each case if the wave motion is transverse, longitudinal or a combination of both.

(a) Motion of a kink in a longitudinal spring produced by displacing one end of the spring sideways.

(b) Waves produced in a cylinder containing a liquid by moving its piston back and forth.

(c) Waves produced by a motorboat sailing in water. 

(d) Ultrasonic waves in air produced by a vibrating quartz crystal.