Decide whether each of the following statements are T-True, or F-False. (If the

Question

Decide whether each of the following statements are T-True, or F-False. (If the first is T and the rest are F, enter TFFFF)

A) If an ideal string can vibrate in a pure standing wave with fundamental frequency f, then (with no changes in length, tension, or material) it can also be made to vibrate in a pure standing wave with a frequency of f/4
B) If you decrease the tension in a string, the frequency of its fundamental vibration will get higher
C) If an ideal string can vibrate in a pure standing wave with frequency f, then (with no changes in length, tension, or material) it can also be made to vibrate in a pure standing wave with frequency of 3f
D) If the fundamental vibration of a string has wavelength lambda, then the next higher mode will have wavelength 2*lambda
E) If you have a standing wave with frequency 5 times the fundamental, there are 4 internal nodes (not counting nodes at the end of the string)

(If the wording of these questions seems unfamiliar, take a look at section 10.1 of the text again.)

Be careful to input your answer as a string of 5 Ts and Fs, in order. (No spaces or any other characters)

Explanation / Answer

A) = false

The fundamental is the lowest frequency resonance, because it corresponds to the longest wavelength that “fits” on the string

B) = false

False. Lower tension means lower wave speed along the string, which means lower frequency

C) = True

The third harmonic has frequency f3 = 3f.

D) = false

The second harmonic has twice the frequency of the fundamental, and therefore half the wavelength since v = f and v is the same for both modes.

E) = True

The 5th mode has 5 antinodes and 4 interior nodes

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