Question

A wave traveling in a string can be described by the function y of xt is equal to 3 times cosine of ( 0.5 times x - 4 times t ) where x is measured in meters, y is measured in centimeters, and t is measured in seconds. What is the speed of this wave?

Answer 1

8 m/s

Step-by-step explanation:

y = 3 Cos (0.5 x - 4 t)

Compare with the standard equation of a wave

`y = A Cos\left ( (2\pi t)/(T)-(2\pi x)/(\lambda ) \right )`

Here, T be the time period, λ be the wavelength and A be the amplitude of the wave.

Let the wave velocity is v.

By comparison

2 π / T = 4

T = 2 π / 4 = π / 2 second = 0.5 π second

And

2 π / λ = 0.5

λ = 2 π / 0.5 = 4 π

use v = f λ = λ / T

v = 4 π / 0.5 π = 8 m/s