Question

A transverse sinusoidal wave of amplitude a, wavelength λ and frequency f is travelling on a stretched string. The maximum speed of any point on the string is v10, where v is the speed of propagation of the wave. If a=10⁻³ m and v = 10 m/s, then λ and f are given by

(A) λ=2π×10⁻² m
(B) λ=10⁻³ m
(C) f = 10³2π Hz
(D) f = 10⁴Hz

Answer 1

The wave speed on a string vibrating at a frequency of 10 Hz and producing a wave with a wavelength of 0.25 m is calculated as 2.5 m/s.

Step-by-step explanation:

The wave speed (v) can be calculated using the wavelength (λ) and frequency (f) of a wave, with the relationship v = fλ. If a string vibrates at a frequency of 10 Hz and produces a transverse wave with a wavelength of 0.25 m, then the wave speed is simply the product of these two values.

To determine the wave speed along the string, multiply the frequency by the wavelength:

v = fλ = 10 Hz × 0.25 m = 2.5 m/s.

Therefore, the speed at which the wave travels along the string is 2.5 meters per second.