B.4) A harmonic wave with a frequency of 80Hz and an amplitude of 0.025m travels along a string to the right with a speed of 12m/s. a) Write a suitable wave function for this wave. b) Find the maximum speed of a point on the string. c) Find the maximum acceleration of a point on the string.

EXPERT ANSWER

Given f=80Hz

Amplitude A= 0.025m

Speed v=12m/s

We know v^2= w^2(A^2-x^2)

Where w=angular frequency=2πf=2(3.1415) (80)

w= 502.6rad/s

A^2-x^2=(v/w) ^2=(12/502.6) ^2

=0.00057

x^2=(0.025) ^2-0.00057

=5.49*10^-5

x=0.0074m

wave function x = A cos wt=0.025 cos 502.6t

Maximum speed vo=Aw

vo=(0.025) (502.6) =12.56 m/s

Maximum acceleration ao=Aw^2

ao=(0.025) (502.6^2)

= 6315m/s^2