An ambulance blowing a siren of frequency 700 Hz is travelling slowly towards a vertical reflecting wall with a speed of 2 ms–1. The speed of sound is 350 ms–1. How many beats are heard per second?
The driver will hear two sounds, one coming directly from the siren and the other reflected at the wall or coming from the acoustic image of the car. V = frequency of direct sound = 700 Hz.
The reflected sound can be imagined to be coming from the mirror image (shown dotted in fig).
The observer (driver) is approaching his image-source which is also approaching with the same speed. Hence u0 = us = u. The frequency of sound heard by him is given by
Since u << v, we can expand
binomially and retain only the
first order terms in u/v.
We then get
The transverse displacement of a string fixed at both ends is given by
Where x and y are in metres and t is in seconds. The length of the string is 1.5 m and its mass is 3.0 × 10–2 kg. What is the tension in the string?
A wire of density ρ is stretched between two clamps a distance L apart, while being subjected to an extension l. Y is the Young’s modulus of the material of the wire. The lowest frequency of transverse vibrations of the wire is given by
A pipe of length 20 cm is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 425 Hz source? The speed of sound = 340 ms –1.
A pipe of length 20 cm is open at both ends. Which harmonic mode of the pipe is resonantly excited by a 1700 Hz source? The speed of sound = 340 ms–1.
A wire has a mass 30 g and linear density 4 × 10 –2 kg m–1. It is stretched between two rigid supports and vibrates in its fundamental mode with a frequency of 50 Hz. What is the speed of transverse waves on the wire?
A steel rod of length 1.0 m is clamped rigidly at its middle. What is the frequency of the fundamental mode for the longitudinal vibrations of the rod? The speed of sound in steel = 5 × 103 ms –1.
Two tuning forks A and B produce 10 beats per second when sounded together. On slightly loading fork A with a little wax, it was observed that 15 beats are heard per second. If the frequency of fork B is 480 Hz, what is the frequency of fork A before it was loaded?
Two sitar strings A and B are slightly out of tune and produce beats of frequency 6 Hz. When the tension in string A is slightly decreased, the beat frequency is found to be reduced to 3 Hz. If the original frequency of A is 324 Hz, what is the frequency of B?
A metal wire of diameter 1 mm is held on two knife edges separated by a distance of 50 cm. The tension in the wire is 100 N. The wire vibrating with its fundamental frequency and a vibrating tuning fork together produce 5 beats per second. The tension in the wire is then reduced to 81 N. When the two are excited, beats are heard at the same rate. What is the frequency of the fork?
Two persons A and B, each carrying a source of sound of frequency V, are standing a few metres apart in a quiet field. A starts moving towards Bwith a speed u. If v is the speed of sound, the number of beats heard per second by A will be