Question:
The equation of a simple harmonic progressive wave travelling on a string is \( y = 8 \sin (0.02 x - 4 t) \) cm. The speed of the wave is ______.
The equation of a simple harmonic progressive wave travelling on a string is \( y = 8 \sin (0.02 x - 4 t) \) cm. The speed of the wave is ______.
Show Hint
Wave speed is \( v = \frac{\omega}{k} \); compare wave equation to \( y = A \sin (kx - \omega t) \).
Updated On: Nov 12, 2025
- 10 cm/s
- 20 cm/s
- 100 cm/s
- 200 cm/s
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Wave equation: \( y = 8 \sin (0.02 x - 4 t) \).
Standard form: \( y = A \sin (kx - \omega t) \).
\[ k = 0.02 \, \text{cm}^{-1}, \quad \omega = 4 \, \text{s}^{-1}. \] Wave speed: \( v = \frac{\omega}{k} = \frac{4}{0.02} = \frac{4 \cdot 100}{2} = 200 \, \text{cm/s}.
Answer: 200 cm/s.
Standard form: \( y = A \sin (kx - \omega t) \).
\[ k = 0.02 \, \text{cm}^{-1}, \quad \omega = 4 \, \text{s}^{-1}. \] Wave speed: \( v = \frac{\omega}{k} = \frac{4}{0.02} = \frac{4 \cdot 100}{2} = 200 \, \text{cm/s}.
Answer: 200 cm/s.
Was this answer helpful?
0
0
Top Questions on Wave Motion
- Two strings with circular cross section and made of same material are stretched to have same amount of tension. A transverse wave is then made to pass through the strings. The velocity of the wave in the first string having the radius of cross section $ R $ is $ v_1 $, and that in the other string having radius of cross section $ R/2 $ is $ v_2 $. Then, $ \frac{v_2}{v_1} $ is:
- JEE Main - 2025
- Physics
- Wave Motion
- A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x-direction in 0.3 sec. The crest P is at $ x = 0 $ at $ t = 0 $ sec and maximum displacement of the wave is 2 cm. Which equation correctly represents this wave?
- JEE Main - 2025
- Physics
- Wave Motion
- The equation of a transverse wave travelling along a string is \( y(x, t) = 4.0 \sin \left( 20 \times 10^{-3} x + 600t \right) \) mm, where \( x \) is in mm and \( t \) is in seconds. The velocity of the wave is:
- JEE Main - 2025
- Physics
- Wave Motion
- The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, $ y_1 (x, t) = 4 \sin(kx - \omega t) $ and $ y_2 (x, t) = 2 \sin(kx - \omega t + \frac{2\pi}{3}) $, are: (Take the angular frequency of initial waves same as $ \omega $)
- JEE Main - 2025
- Physics
- Wave Motion
- The frequency of a wave is 500 Hz and its wavelength is 0.66 m. What is the speed of the wave?
- AP EAPCET - 2025
- Physics
- Wave Motion
View More Questions
Questions Asked in Maharashtra Class XII exam
- What is value of B called, when H = 0 is in the hysteresis loop?
- If \(|\vec{a}| = 5\), \(|\vec{b}| = 13\), and \(|\vec{a} \times \vec{b}| = 25\), then \(|\vec{a} \cdot \vec{b}|\) is equal to ........
- Maharashtra Class XII - 2025
- Vector Algebra
- Calculate the electric field intensity at a point just near the surface of a charged plane sheet, measured from its mid-point. [ \( \sigma = 8.85 \, \mu C/m^2 \) ]
- Maharashtra Class XII - 2025
- Electrostatics
- Identify ‘A’ and ‘B’ in the following reaction and rewrite the complete reaction : \[ \text{CH}_3\text{-CH=CH}_2 \xrightarrow[\text{Peroxide}]{\text{HBr}} \text{A} \xrightarrow[\text{-KBr}]{\text{alcoholic KCN}} \text{B} \]
- Maharashtra Class XII - 2025
- Organic Chemistry
- Divide the number 20 into two parts such that the sum of their squares is minimum.
- Maharashtra Class XII - 2025
- Optimization
View More Questions