A string of length 100 cm is held fixed at both ends and vibrates in a standing wave pattern.The wavelengths of the constituent traveling waves CANNOT be:
A)400 cm
B)200 cm
C)100 cm
D)67 cm
E)50 cm

Question

Quizplus · Accepted Answer

The wavelength of a standing wave on a string fixed at both ends is equal to twice the length of the string divided by an odd integer (n), where n represents the harmonic number. Thus, the possible wavelengths for this string are:

First harmonic: λ1 = 2L/1 = 200 cm
Second harmonic: λ2 = 2L/3 = 67 cm
Third harmonic: λ3 = 2L/5 = 40 cm
Fourth harmonic: λ4 = 2L/7 = 29 cm
Fifth harmonic: λ5 = 2L/9 = 22 cm

Therefore, the wavelength of 400 cm is not possible for this string because it is not equal to twice the length divided by an odd integer, and thus cannot represent a standing wave on this string.

A String of Length 100 Cm Is Held Fixed at Both