Question 311: Waves

Question

Prong of a vibrating tuning fork is in contact with water surface. It produces concentric circular waves on the surface of water. The distance between five consecutive crests is 0.8 m and the velocity of wave on the water surface is $56 \mathrm{~m} / \mathrm{s}$. The frequency of tuning fork is

Accepted Answer

Let's break down the problem step by step:
The phrase "distance between five consecutive crests" means the distance covering four wavelengths (since there are four intervals between five points). Thus, if we denote the wavelength by $$\lambda$$, then:
$$4\lambda = 0.8\, 	ext{m}$$
Solve for $$\lambda$$:
$$\lambda = \frac{0.8\, 	ext{m}}{4} = 0.2\, 	ext{m}$$
The relationship between wave velocity, frequency, and wavelength is given by:
$$v = f 	imes \lambda$$
where
$$v$$ is the velocity (56 m/s)
$$\lambda$$ is the wavelength (0.2 m)
$$f$$ is the frequency we are finding.
Rearrange the formula to solve for frequency:
$$f = \frac{v}{\lambda}$$
Substitute the given values:
$$f = \frac{56\, 	ext{m/s}}{0.2\, 	ext{m}} = 280\, 	ext{Hz}$$
So, the frequency of the tuning fork is $$280\, 	ext{Hz}$$, which corresponds to Option B.

Answer

256 Hz

Answer

280 Hz

Answer

341 Hz

Answer

512 Hz

Waves

Prong of a vibrating tuning fork is in contact with water surface. It produces concentric circular waves on the surface of water. The distance between five consecutive crests is 0.8 m and the velocity of wave on the water surface is 56 \mathrm{~m} / \mathrm{s}. The frequency of tuning fork is

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