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Answer :
Final answer:
The question asks for various measurements related to waves on a violin string and sound waves emitted by the string. Unfortunately, the question doesn't provide enough information to determine the speed of waves on the string or the tension in the string. However, we can still find the wavelength of waves on the string and the wavelength of sound waves emitted by the string using the given frequencies and lengths.
Explanation:
To find the speed of waves on a violin string, we can use the formula v = √(F/m), where v is the speed, F is the tension in the string, and m is the mass per unit length of the string. Given the length of the string, we can find the wavelength using the formula λ = 2L/n, where λ is the wavelength and n is the harmonic number. Finally, the speed of sound in air can be used to find the wavelength of the sound waves emitted by the string using the formula v = fλ, where f is the frequency of the sound waves.
- (a) Speed of waves on the violin string:
- To find the speed of waves on the string, we need to know the tension in the string. Unfortunately, the given question does not provide the tension. Hence, we cannot determine the speed of waves on the string without this information.
- (b) Tension in the string:
- Without the tension, we cannot calculate it either.
- (c) Wavelength of waves on the string:
- The fundamental frequency of the string is given as 978 Hz. The harmonic number for the fundamental is 1. Using the formula, λ = 2L/n, where L is the length of the string and n is the harmonic number, we can calculate the wavelength. Substituting the values, we get λ = 2 * 24.8 cm / 1 = 49.6 cm.
- (d) Wavelength of sound waves emitted by the string:
- Given the speed of sound in air as 343 m/s and the frequency of the sound waves as 978 Hz, we can use the formula v = fλ to find the wavelength. Rearranging the formula, we get λ = v / f. Substituting the values, we get λ = 343 m/s / 978 Hz = 0.35 m.
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