Question

A string that is fixed at both ends has a length of 1.56 m. When the string vibrates at a frequency of 70.1 Hz, a standing wave with five loops is formed. (a) What is the wavelength of the waves that travel on the string? (b) What is the speed of the waves? (c) What is the fundamental frequency of the string?

Answer 1

Answer:

(a).The wavelength of the waves is 0.624 m.

(b). The speed of the waves is 43.74 m/s.

(c). The fundamental frequency of the string is 14.02 Hz.

Explanation:

Given that,

length = 1.56 m

Frequency = 70.1 Hz

Number of loop = 5

(a). We need to the calculate the wavelength of the waves

Using formula of wave length

$\lambda=\dfrac{2L}{n}$

Put the value into the formula

$\lambda=\dfrac{2\times1.56}{5}$

$\lambda=0.624\ m$

(b). We need to calculate the speed of the waves

Using formula of speed

$v= \lambda\times f$

Put the value into the formula

$v=0.624\times70.1$

$v=43.74\ m/s$

(c). We need to calculate the fundamental frequency of the string

Using formula of fundamental frequency

$f'=\dfrac{f}{n}$

Put the value into the formula

$f'=\dfrac{70.1}{5}$

$f'=14.02\ Hz$

Hence, (a).The wavelength of the waves is 0.624 m.

(b). The speed of the waves is 43.74 m/s.

(c). The fundamental frequency of the string is 14.02 Hz.