Question 128: Waves

Question

The equation of a wave travelling on a string is y = sin[20πx + 10πt], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

Accepted Answer

The equation for a wave traveling on a string is given by $ y = \sin(20\pi x + 10\pi t) $, where $ x $ is the distance and $ t $ is the time in SI units. To find the minimum distance between two points having the same oscillating speed, we use the concept that this distance is half the wavelength $\left(\frac{\lambda}{2}ight)$.
To find the wavelength $\lambda$:
$ \lambda = \frac{2\pi}{k} $
Here, the wave number $ k = 20\pi $. Thus,
$ \lambda = \frac{2\pi}{20\pi} = \frac{1}{10} 	ext{ m} = 10 	ext{ cm} $
Thus, the minimum distance between two points having the same speed is:
$ 	ext{Distance} = \frac{\lambda}{2} = \frac{10 	ext{ cm}}{2} = 5 	ext{ cm} $

Answer

10 cm

Answer

2.5 cm

Answer

20 cm

Answer

5.0 cm

Waves

The equation of a wave travelling on a string is y = sin[20πx + 10πt], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

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