When a tuning fork is held over the open end of a very thin tube, as in the figure below, the smallest value of L that produces resonance is found to be 33.0 cm.
(a) What is the wavelength of the sound? [Hint: Assume that the displacement antinode is at the open end of the tube.]
(b) What is the next larger value of L that will produce resonance with the same tuning fork?
cm
(c) If the frequency of the tuning fork is 277 Hz, what is the speed of sound in the tube?
m/s
Could someone please help me out on this.Thank you! I need a good explanation on this please.
Certainly! Let's break down each part of the question step by step.
(a) To find the wavelength of the sound, we can use the formula:
λ = 4L
Where λ represents the wavelength and L represents the length of the tube. In this case, L is given as 33.0 cm (which we'll convert to meters later). Plugging in the values:
λ = 4 * 0.33 m
Calculating the result:
λ = 1.32 m
So, the wavelength of the sound produced by the tuning fork is 1.32 meters.
(b) To find the next larger value of L that will produce resonance with the same tuning fork, we need to consider that for resonance, the length of the tube must be an odd multiple of one-fourth of the wavelength. In other words:
L = (2n + 1) * (λ/4)
Where n is a positive integer representing the harmonic number. Since we're looking for the next larger value, we can set n = 1. Substituting the given wavelength:
L = (2 * 1 + 1) * (1.32 m / 4)
Calculating the result:
L = 0.99 m
So, the next larger value of L that will produce resonance with the same tuning fork is 0.99 meters.
(c) To determine the speed of sound in the tube, we can use the formula:
v = f * λ
Where v represents the speed of sound, f represents the frequency of the tuning fork, and λ represents the wavelength which we found to be 1.32 meters. Given f as 277 Hz:
v = 277 Hz * 1.32 m
Calculating the result:
v = 365.64 m/s
Therefore, the speed of sound in the tube is approximately 365.64 meters per second.
I hope this helps! Let me know if you have any further questions.