A fellow student of mathematical bent tells you that the wave function of a trav

Question

A fellow student of mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x,t)=2.30mmcos[(6.98rad/m)x+(742rad/s)t]. Being more practical-minded, you measure the rope to have a length of 1.35 m and a mass of 3.38 grams. Assume that the ends of the rope are held fixed and that there is both this traveling wave and the reflected wave traveling in the opposite direction.

A) What is the wavefunction y(x,t) for the standing wave that is produced?

B) In which harmonic is the standing wave oscillating?

C) What is the frequency of the fundamental oscillation?

Explanation / Answer

Here,

y(x,t)= 2.30mm cos[(6.98rad/m)x+(742rad/s)t]

length , L = 1.35 m

a)

the wavefunction of the standing wave is

y(x,t)= 2.30mm cos[(6.98rad/m)x+(742rad/s)t]

y = A *cos(w *t + k * x)

B)

speed of wave = w/k

speed of wave = 742/6.98 m/s

speed of wave = 106.3 m/s

wavelength = 2 * L

wavelength = 2 * 1.35

wavelength = 2.70 m

fundamental frequency , f0 = 106.3/2.70 Hz

f0 = 39.4 Hz

frequency = 742/2pi

frequency = 118.11 Hz

number of harmonic = 118.11/39.4

number of harmonic = 3

the number of harmonic is 3

c)

fundamental frequency = f0

fundamental frequency = 39.4 Hz

the frequency of the fundamental oscillation is 39.4 Hz

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