Question

You have a 1.99-m-long stretched string with a mass of 20.1 g. When you oscillate the string at 440 Hz, which is the frequency of the standard A pitch that orchestras tune to, you observe transverse waves with a wavelength of 15.7 cm traveling along the string. Calculate the tension in the string. Number

Answer 1

We know that, Ft force of tension

Ft = mv^2/L

We also know that, v = nf

where, n = 0.157 m

f = 440 Hz

v = 0.157*440 = 69.1 m/s

Ft = mv^2/L

= 0.0201*69.1^2/1.99

= 48.23 N. answer

Answer 2

The strategy here is to use the given frequency and wavelength to find the speed of transverse waves in the stretched string and to then use the wave speed and the string's given mass and length to find its tension.

For a periodic wave, the wave speed ?$v$, frequency ?$f$, and wavelength ?$\lambda$ are related by

$$v=f\lambda$$

The speed ?$v$ of transverse waves in a stretched string is given by

$$v=\sqrt{\frac{T}{\left(\frac{m}{L}\right)}}$$

where ?$T$ is the string's tension and ?$m$ and ?$L$ are its mass and length, respectively.

Equate the two expressions for ?$v$ and solve for the tension ?$T$ in terms of given quantities.

$$T=\frac{m{f}^2{\lambda }^2}{L}$$

In order to obtain the numerical answer, convert the given values to the appropriate SI units where necessary and substitute them into the expression for ?$T$.

?=(0.0197 kg)(440 Hz)2(0.155 m)2(2.05 m)=44.7 N