The wave function for a traveling wave on a taut string is (in SI units)(a) What

wurmiana6d

wurmiana6d

Answered question

2021-11-15

The wave function for a traveling wave on a taut string is (in SI units)(a) What are the speed and direction of travel of the wave? (b) What is the vertical position of an element of the string at t = 0, x = 0.100 m? What are (c) the wavelength and (d) the frequency of the wave? (e) What is the maximum transverse speed of an element of the string? y(x,t)=(0.350m)sin(10π3πx+π4)

Answer & Explanation

pseudoenergy34

pseudoenergy34

Beginner2021-11-16Added 22 answers

Knows:
The wave function is y(x,t)=(0.350 m)sin(10πt3πx+π4)
Calculations
a) The wave speed is v=wk, where w is the angular frequency, and k is the angular number. We can read values of w and k from general form of the sinusoidal wave function y=sin(kxwt+ϕ):w=10πrads and k=3πradm. So, the wave speed is:
v=10πrads3πradm
v=3.33ms
The direction of the wave propagation is positive x, according to equations 16.1, 16.5 and 16.10.
b) At t=0 and x=0.100 m, vertical position of the element is:
y(x,0)=(0.350m)sin(10πt3πx+π4)
=(0.350m)sin(10π×03×3.14×0.100m+π4)
=(0.350m)sin(10π×03×3.14×0.100m+π4)
=(0.350n)sin(0.157)
=0.350m×(0.156)
=0.055m
=5.5cm
c) The wavelength λ is λ=2πk, and the frequency f is f=w2π
λ=2π rad3π radm=0.667m
f=10πrads2π rad=5Hz
d) The maximum transvers speed of an element on the string is vmax,y=ωA, where A=0.350m is the amplitude.
So: vmax,y=10×3.14rads×0.350 m=11.0ms

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