Question

A sound produces 15 crests and 15 troughs in 3 sec. When the second crest is produced, the first crest is 2 cm away from the source. Calculate the frequency, wavelength and the speed of the wave.

Answer 1

15 cycles =3sec

we know ,
time period is the time taken by wave for complete one cycle.

so,
T = 3sec/15 = 0.2 sec

we also know ,
frequency : - no of oscillation per second.
e.g f = 1/T = 1/0.2 =5Hz

wavelength :- linear separation between two consecutive crest or trough .

so,
wavelength = 2 cm

speed of wave =frequency x wavelength

= 5 x 2 =10 m/s

Answer 2

Given:
Time taken to produce 15cycles=3sec
Time period=time taken by the wave to complete one cycle/oscillation]=T=
3/15=0.2sec
Frequency=1/Time period⇒1/T⇒1/0.2⇒5hertz
As wavelength is the distance between two consecutive crests or troughs, so
λ=2cm
Speed of Sound wave: V=frequency x wavelength
V=5x2=10cm/s
∴Frequency, Wavelength and Speed of sound wave are 5Hz , 2cm and 10cm/s respectively.