Question

A wave along a string has the following equation $y = 0.05 \sin (28t - 1.78x)\, m$ (where t is in seconds and x is in meters). What are the amplitude, (A) frequency (f) and wavelength $(\lambda)$ of the wave?

• A. amplitude = 0.05 m, frequency = 4.456 Hz and wavelength $\lambda$ =3.518 m
• B. amplitude = 0.05 m, frequency = 28 Hz and wavelength$\lambda$=2.0 m
• C. amplitude = 5.0 m, frequency = 4.456 Hz and wavelength $\lambda$ =3.518 m
• D. amplitude = 0.05 m, frequency = 2.0 Hz and wavelength $\lambda$= 28 m
• E. amplitude = 0.05 m, frequency = 3.456 Hz and wavelength $\lambda$=4.518 m

Answer 1

Answer: (A)

Given the equation of wave along string
$y=0.05 \sin (28 t-1.78 x)$...(i)
The general equation of a wave is given as
$y=A \sin (\omega t-k x)$...(ii)
Now, comparing Eqs. (i) and (ii), we get
Amplitude, $ A=0.05\, m ,\, k=1.78$
and $\omega=28$
$\Rightarrow $ Frequency, $f=\frac{\omega}{2 \pi}=\frac{28}{2 \pi}=4.456\, Hz$
and wavelength, $\lambda=\frac{2 \pi}{k}=\frac{2 \pi}{1.78}=3.529\, m$