# Measuring the Velocity of Sound Applying a Standing Wave of a String – Lab Report Example

The paper “ Measuring the Velocity of Sound Applying a Standing Wave of a String”   is an intriguing version example of a lab report on physics. The purpose of this experiment was to delve into standing waves on a string and to establish the relationship between the velocity of a wave in vibrating string and its characteristics including; mass per unit length, frequency, and tension. A relationship exists between these characteristics and the speed of a wave. Theoretically, the velocity of a standing wave on a string can be determined using the formula; Where; is the tension of the string is the velocity of the standing wave is the linear mass density is the mass of the string is the length of the string This relationship can be determined experimentally and it was the main objective of the experiment. 1.1 Aims The purpose of this experiment was to: Establish the relationship between various characteristics of a vibrating string and velocity of the resultant standing wave. Develop research skills. An understanding of standing waves. Investigate the speed of sound in a string. 2.0 Standing Waves A wave is a traveling disturbance carrying energy as it propagates away from the source (Giordano, 2012: 384).

Waves can be classified into either transverse or longitudinal. The vibration of particles for a transverse wave is perpendicular to the direction of propagation of wave while for longitudinal wave the direction of particle vibration is in parallel to the direction of propagation of the wave. Plucking a string under tension will result in the production of transverse waves. If there is a continuous production of transverse waves from the source, they will be away at the other fixed end of the string.

Interference occurs between the incident wave and the reflected wave when they meet and will result in a standing wave. Standing wave on a string Various properties of waves such as the position of particles can be used to describe a transverse wave. The maximum distance above or below the equilibrium position of wave-particle travel in a transverse wave is referred to as amplitude (Giordano, 2012: 458). Wavelength () of a wave is the horizontal distance two successive points and it is the distance of one cycle of a wave (Giordano, 2012: 458).

The time taken by one complete cycle of a transverse wave is referred to as period usually abbreviated as. The total number of cycles in one second is referred to as frequency usually abbreviated as. Frequency can also be obtained from reciprocal of the period. These properties of waves can be used to determine the velocity of a wave. . .... .... .... (i) In a single wavelength, the horizontal distance while the change in time. Substituting these values in equation (i), then we shall have; or Therefore, the speed of a wave is dependent on wavelength, frequency, and period. The velocity of a transverse wave on a string is also dependent on tension in the string and mass per unit length (properties of the string used) (Giordano, 2012: 390).

From Newton’ s second law, force is directly proportional to acceleration. Under high tension, a string will have its inter-particle force being very high. Therefore, Newton’ s second law tension which is a force will affect the velocity of a wave on a string. Velocity will be directly proportional to the tensional force. Similarly, the mass of the particles affects how it responds to the pulling force as a result of vibration.

A string with greater mass per unit length will respond slowly thus moves with less velocity (Giordano, 2012: 460). Therefore, the velocity of a wave is inversely proportional to mass per unit length of a string simply known as linear density. In point of fact, a direct proportionality exists between velocity and the square root of these quantities.

References

5.0 References

Giordano, N. College Physics, Vol 1 (ed 2). New York: Cengage Learning. 2012. Print.