Question

A device called oscillator is used to send waves along a stretched string. The string is 20 cm long, and four complete waves fit along its length when the oscillator vibrates 30 times per second. For the waves on the strings.

(a) what is their wavelength?
(b) what is their frequency
(c) what is their speed?

Answer 1

(a) Given that there are four complete waves. So,
Wavelength = ${\displaystyle \frac{\text{Total length of string}}{\text{Number of waves}}}$
Therefore , 
Wavelength = ${\displaystyle \frac{20}{4}}$ cm
= 5 cm 
= 0.05 m
(b) We have to calculate frequency. We know,
Frequency = (Vibration per second) × (Number of complete waves formed)
Therefore frequency,
Frequency = (30) × (4) Hz
                  = 120 Hz
(c) Now we have to calculate the velocity of the wave.
Given: Frequency f = 120 Hz
Wavelength λ = 0.05 m
We know the relation between velocity, frequency, and wavelength
ν = f × λ,
where ν is the velocity, f the frequency, and λ the wavelength.
Therefore,
ν = (120) × (0.05) m/s
   = 6 m/s
Therefore, velocity of the wave is 6 m/s.