You observe a 1 meter long guitar string vibrating. a) Noting that there are two

Question

You observe a 1 meter long guitar string vibrating.

a) Noting that there are two nodes, not counting the ends, determine the wavelength of the underlying traveling waves producing the standing waves.

b) Next, you instead invoke a vibration on this same string that has only one node not counting the fixed ends, and observe that the frequency is

1000 Hz. What then must be the corresponding underlying traveling wave speed?

c) Determine the period of oscillation for any string element in the circumstance of part a.

Explanation / Answer

given L = 1 m

so, no of loops, N = 3

a) wavelength, lamda = 2*L/N

= 2*1/3

= 0.667 m

b)

wavelength, lamda = 2*L/N

= 2*1/2

= 1m

now use, v = lamda*f

= 1*1000

= 1000 m/s

c) T = 1/f

= 1/1000

= 10^-3 s

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