### Waves - Result Question 5

#### 5. A wave in a string has an amplitude of $2 cm$. The wave travels in the + ve direction of $x$ axis with a speed of $128 m / sec$ and it is noted that 5 complete waves fit in $4 m$ length of the string. The equation describing the wave is

[2009]

(a) $y=(0.02) m \sin (15.7 x-2010 t)$

(b) $y=(0.02) m \sin (15.7 x+2010 t)$

(c) $y=(0.02) m \sin (7.85 x-1005 t)$

(d) $y=(0.02) m \sin (7.85 x+1005 t)$

## Show Answer

#### Answer:

Correct Answer: 5. (c)

Solution:

- (c) $A=2 cm, \frac{\omega}{k}=128 ms^{-1}, 5 \lambda=4, \lambda=$

$ \frac{4}{5} m $

$y=A \sin (k x-\omega t)$,

$k=\frac{2 \pi}{\lambda} \Rightarrow \frac{2 \pi \times 5}{4}=\frac{31.4}{4}=7.85$

$y=0.02 m \sin (7.85 x-1005 t)$

$\omega=128 \times 7.85=1005$