Question

To what tension (in newtons) must you adjust the screw so that a transverse wave of wavelength 3.33 cm makes 621 vibrations per second?

Answer 1

Answer:

T=9.4 N

Explanation:

We are given that

Mass of wire,m=16.5 g=$\frac{16.5}{1000}$kg

1 kg=1000g

Length of wire,l=75 cm=$75\times 10^{-2}$m

1 m=100 cm

Wavelength of transverse wave=$\lambda=3.33 cm=3.33\times 10^{-2}$m

Frequency=$621 Hz$

Mass per unit length=$m_l=\frac{m}{l}=\frac{16.5}{1000\times 75\times 10^{-2}}=0.022 kg/m$

$\nu=\frac{v}{\lambda}$

$v=\nu \lambda$

Where$\nu=$frequency of wave

$\lambda$=Wavelength of wave

Speed of wave=v

Using the formula

$v=3.33\times 10^{-2}\times 621=20.7m/s$

$v=\sqrt{\frac{T}{m_l}}$

$v^2=\frac{T}{m_l}$

$T=v^2m_l$

Using the formula

$T=(20.7)^2\times 0.022=9.4N$

Hence, the tension,T=9.4 N