356
8 Waves
pitched whistle at 1.5 m/s. Find the beat frequency that he hears. Assume the
sound velocity of 330 m/s.
8.82 A tuning fork of frequency 300 c/s gives 2 beats/s with another fork of
unknown frequency. On loading the unknown fork the beats increase to 5/s,
while transferring the load to the fork of known frequency increases the number of beats per second to 9. Calculate the frequency of the unknown fork
(unloaded) assuming the load produces the same frequency change in each
fork.
[University of Newcastle]
8.2.10 Waves in Pipes
8.83 An open organ pipe sounding its fundamental note is in tune with a fork of
frequency 439 cycles/s. How much must the pipe be shortened or lengthened
in order that 2 beats/s shall be heard when it sounded with the fork? Assume
the speed of sound is 342 m/s.
[University of Durham]
8.84 A light pointer fixed to one prong of a tuning fork touches a vertical plate.
The fork is set vibrating and the plate is allowed to fall freely. Eight complete oscillations are counted when the plate falls through 10 cm. What is the
frequency of the tuning fork?
[Indian Institute of Technology 1997]
8.85 Air in a tube closed at one end vibrates in resonance with tuning fork whose
frequencies are 210 and 350 vibrations/s, when the temperature is 20 ◦ C.
Explain how this is possible and find the effective length of the tube. Assume
that the velocity in air at 0 ◦ C is 33, 150 cm/s.
[University of London]
8.86 An open organ pipe is suddenly closed with the result that the second overtone
of the closed pipe is found to be higher in frequency by 100 vibrations/s than
the first overtone of the original pipe. What is the fundamental frequency of
the open pipe?
[University of Bristol]
8.3 Solutions
8.3.1 Vibrating Strings
8.1 The one-dimensional wave equation is
∂ 2 y
∂ x 2 =
1
v 2
∂ 2 y
∂t 2
(1)
8 Waves
pitched whistle at 1.5 m/s. Find the beat frequency that he hears. Assume the
sound velocity of 330 m/s.
8.82 A tuning fork of frequency 300 c/s gives 2 beats/s with another fork of
unknown frequency. On loading the unknown fork the beats increase to 5/s,
while transferring the load to the fork of known frequency increases the number of beats per second to 9. Calculate the frequency of the unknown fork
(unloaded) assuming the load produces the same frequency change in each
fork.
[University of Newcastle]
8.2.10 Waves in Pipes
8.83 An open organ pipe sounding its fundamental note is in tune with a fork of
frequency 439 cycles/s. How much must the pipe be shortened or lengthened
in order that 2 beats/s shall be heard when it sounded with the fork? Assume
the speed of sound is 342 m/s.
[University of Durham]
8.84 A light pointer fixed to one prong of a tuning fork touches a vertical plate.
The fork is set vibrating and the plate is allowed to fall freely. Eight complete oscillations are counted when the plate falls through 10 cm. What is the
frequency of the tuning fork?
[Indian Institute of Technology 1997]
8.85 Air in a tube closed at one end vibrates in resonance with tuning fork whose
frequencies are 210 and 350 vibrations/s, when the temperature is 20 ◦ C.
Explain how this is possible and find the effective length of the tube. Assume
that the velocity in air at 0 ◦ C is 33, 150 cm/s.
[University of London]
8.86 An open organ pipe is suddenly closed with the result that the second overtone
of the closed pipe is found to be higher in frequency by 100 vibrations/s than
the first overtone of the original pipe. What is the fundamental frequency of
the open pipe?
[University of Bristol]
8.3 Solutions
8.3.1 Vibrating Strings
8.1 The one-dimensional wave equation is
∂ 2 y
∂ x 2 =
1
v 2
∂ 2 y
∂t 2
(1)