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
Where A is the area of cross-section of the wire. Thus
Now, mass per length of the wire
The lowest frequency (i.e. frequency of the fundamental mode) is given by
Using (i) and (ii) in this we get
Two organ pipes, each closed at one end, give 5 beats per second when emitting their fundamental notes. If their lengths are in the ratio of 50 : 51, their fundamental frequencies (in Hz) are
Two sources A and B are sounding notes of frequency 680 Hz. A listener moves from A to B with a constant velocity u. If the speed of sound is 340 ms –1, what must be the value of u so that he hears 10 beats per second?
A hospital uses an ultrasonic scanner of frequency 3.2 MHz to locate tumours in a tissue. What is the wavelength of ultrasonic waves in a tissue in which the speed of the waves is 1.6 km s–1?
A bat flying above a take emits ultrasonic sound of 100 kHz. When this wave falls on the water surface, it is partly reflected and partly transmitted. What are the wavelengths of the reflected and transmitted waves? The speed of sound in air is 340 ms –1 and in water 1450 ms–1.
The particle displacements in a travelling harmonic wave are given by
Where x and y are in centimeters and t is in seconds. What is the phase difference between oscillatory motion at two points separated by a distance of 4 m?
A string of length 10.0 m and mass 1.25 kg is stretched with a tension of 50 N. If a transverse pulse is created at one end of the string, how long does it take to reach the other end?
A uniform metal wire of density ρ, cross-sectional area A and length L is stretched with a tension T. The speed of transverse wave in the wire is given by
Standing waves are produced by the superposition of two waves
Where x and y are expressed in metres and t is in seconds. What is the amplitude of a particle at x = 0.5 m. Given
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 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.