Transverse waves on a string have a velocity of 15 m/s, amplitude of 0.10m and a wavelength of 25 cm. The waves travel in the +x direction and at t=0 the x=0 end of the string is at a maximum upward displacement. Find the Period of the wave (sec):
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
![### Transverse Waves on a String
**Wave Characteristics:**
- **Velocity:** 15 m/s
- **Amplitude:** 0.10 m
- **Wavelength:** 25 cm
The waves travel in the positive x direction, and at time \( t = 0 \), the x = 0 end of the string is at a maximum upward displacement.
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**Problem:**
Find the Period of the Wave (in seconds):
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### Detailed Explanation:
**Given Data:**
- **Velocity (\(v\)):** 15 m/s
- **Wavelength (\( \lambda \)):** 25 cm (0.25 m)
The period \( (T) \) of the wave can be found using the relationship between the velocity, wavelength, and period of a wave, which is given by:
\[ v = \frac{\lambda}{T} \]
Rearranging to solve for the period \( T \):
\[ T = \frac{\lambda}{v} \]
Substituting the given values:
\[ T = \frac{0.25 \, \text{m}}{15 \, \text{m/s}} = \frac{0.25}{15} \, \text{s} = 0.0167 \, \text{s} \]
**Answer:**
The period of the wave is \( 0.0167 \) seconds.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdfe80350-6fa1-469d-aae2-95b4dd3aa499%2F6999008e-fffb-49eb-8fa2-7189eafe52d4%2Fl1aup6_processed.png&w=3840&q=75)
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