The vibrations of a string fixed at both ends are described by the equation $y = (5.00 m m)$ $sin [(1.57 c m^{- 1}) x] sin [(314 s^{- 1}) t]$ . What are the wavelengths and the wave speeds of the two transverse waves that combine to give vibration?

4, 2

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5, 2

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4, 3

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5, 3

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Solution

The correct option is A $4, 2$
From the given equation, the wave number $K = 1.57 c m^{- 1}$ and angular frequency $ω = 314 s^{- 1}$ , the wavelength is

$λ = \frac{2 π}{k} = \frac{2 \times 3.14}{1.57}$

$λ = 4.00$ cm and the frequency is

$n = \frac{ω}{2 π} = \frac{314}{2 \times 3.14} = 50 s^{- 1}$

Now the wave speed is

$v = n λ = (50 s^{- 1}) (4.00 c m) = 2.00 m / s$ .

Suggest Corrections

Similar questions

y = (5.00 m m)

sin [(1.57 c m^{- 1}) x] sin [(314 s^{- 1}) t]

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y = (5.00 m m)

sin [(1.57 c m^{- 1}) x] sin [(314 s^{- 1}) t]

10.0 c m

The vibrations of a string fixed at both ends are described by the

$y = (5.00 m m) s i n [(1.57 c m^{- 1}) x] s i n [(314 s^{- 1}) t]$

If the length of the string is 10.0 cm, locate the nodes and the antinodes. How many loops are formed in the vibration?

The equation for the vibration of a string, fixed at both ends vibrating in its third harmonic, is given

$y = (0.4 c m) s i n [(0.314 c m^{- 1}) x] c o s [(600 π s^{- 1}) t]$

i. What is the frequency of vibration?

ii. What are the positions of the nodes?

iii. What is the length of the string?

iv. What is the wavelength and the speed of two travelling waves that can interfere to give this vibration?

y = (0 \cdot 4 cm) \sin [(0 \cdot 314 {cm}^{- 1}) x] \cos [(600 π s^{- 1}) t]

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