what is the harmonic number of this wave? Physics II QUIZ 12: Interference of Li

Question

what is the harmonic number of this wave?

Physics II QUIZ 12: Interference of Light Questions 111-115 refer to the following situation shown in Figure 16 A standing wave is produced along a string driven by a resonant frequency as shown on the picture below. Measured frequency of this standing wave is 51.0Hz. The vibrating length of string i 76.2 cm, L 76.2 cm Figure 16: Vibrating String 111. What is the harmonic number of this wave? (E) 5 (C) 3 (A) 1 (B) 2 112. What is the wavelength of the standing wave formed along a string as shown on the picture? (E) 50.8 m (C) 0.965 m (D) 5.10 m (A) 0.254 m (B) 0.508 m 113. How much tension is applied to the string shown in Figure 16, if its linear density is 1.80 x 10 kg/m? (E) 1.3 N (D) 0.860 N (B) 0.271 N (C) 0.121 N (A) 0.005 N 114. What is the fundamental frequency of the string? (D) 34 Hz (A) 153 Hz (C) 51 Hz (E) 17 Hz (B) 124 Hz 115. What needs to be done to the string to increase its fundamental frequency without changing its length or mass? (A) It cannot be done because the fundamental frequency relates only to the length of a string (B) The tension on the string needs to be decreased (C) The tension on the string needs to be increased (D) A certain frequency needs to be applied (E) I have no idea

Explanation / Answer

111 -- C

the harmonic is third harmonic and also called second overtone of the standing wave on string

112 --- B
   wavelength of the standing wave formed is

   here is L = 3*lambda/2 ==> lambda = 2*L/3 = 2*0.762/3 m = 0.508 m

113--- C

   given measured frequency is f = 51 Hz, wavelength LAmbda = 0.508 m

   v = lambda*f = 0.508*51 m/s = 25.908 m/s

and also from the formula for speed of wave on string is

   V = sqrt(T/mue)

   T = V^2*mue

   T = 25.908^2*1.8*10^-4 N

   T = 0.12082040352 N

   T = 0.121 N

114 -----E

   fundamental frequencyof the string is f= v/2L = 25.908/2*0.762 HZ = 17 HZ

115 -- C

   Tension should be increased

   f= v/2L = sqrt(T/mue)/2L

   L, mue are constant then

   f increased if T increases so answer i s C

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