University:
University of Cambridge
Course:
0625 IGCSE | Physics
Academic year:

2023
Views:

22

Pages:

2
Author:

Deddy A.

Velocity of Waves on Strings V= F. T (for transverse waves) - depends on string tension + string density greater tension F → greater wave speed, b/c period of vibration is shorter & the wave advances one wavelength during the period. tuning guitar strings by tightening →String w/ greater mass/unit (p) vibrates more slowly longer period slower ware speed linear density N = M/L EXAMPLE 13.10 A PULSE TRAVELING ON A STRING GOAL: Calculate the speed of a wave on a string. PROBLEM: A uniform string has a mass M of 0.030 0 kg and a length L of 6.00 m. Tension is maintained in the string by suspending a block of mass m 2.00 kg from one end (Fig. 13.28). (a) Find the speed of a transverse wave pulse on this string. (b) Find the time the pulse travels from the wall to the pulley. Neglect the mass of the hanging part of the string. 1.00 m 2.00 kg STRATEGY The tension can be obtained from Newton's second law for equilibrium applied to the block and the mass per unit length of the string is µ = M/L. With these quantities, the speed of the transverse pulse can be found by substituting Equation 13.18. Part (b) requires the formula d = vt. Figure 13.28 (Example 13.10) The string's tension is maintained by the suspended block. The wave speed is given by the expression = = VF/. a.) Ms 1 string = 0.03 kg 19.6 N L = 6 m mblock 2 kg F = Fr-mg=0 62.6175 N = 0.03 kg: 5×10-3 kg/ 6m na b.) t=dt= Fr-(2kg) (9.8) FT = 19.6 N 62.61m/s 0.0799 s Interference of Waves 2 traveling waves can meet pass thru each other w/o being destroyed/altered Principle of Superposition: When two or more traveling waves encounter each other, the resultant wave is found by adding together the displacements of the individual waves point by point. * valid only when individual waves have small amps. Crests of A & B line up same freq., but *2 amplitude. Combining the two waves in parts (a) and (b) results in a wave with twice the amplitude. Figure 13.29 Constructive interfer ence. If two waves having the same frequency and amplitude are in phase, as in (a) and (b), the resultant wave when they combine (c) has the same frequency as the individual waves, but twice their amplitude. "in phase" constructive interference. same freqs. crests of A line up w/ troughs in B Destructive interference. superposition of waves. 180 out of phase Combining the waves in (a) and (b) results in complete cancellation. Figure 13.30 Destructive interfer ence. The two waves in (a) and (b) have the same frequency and ampli- tude but are 180 out of phase.