Question

Question 4 to 11 plz Dr?

Standing Waves on a String Physics Topics If necessary, review the following topics and relevant textbook sections from Serway / Jewett "Physics for Scientists and Engineers", 9th Ed. • Mathematics of Traveling Waves (Serway 17.2) • Speed of Waves on a String (Serway 17.3) • Superposition of Waves (Serway 18.1) • Standing Waves on a string (Serway 18.2, 18.3) Introduction Imagine two sinusoidal traveling waves with equal amplitudes and frequencies moving in opposite directions. These waves are described mathematically by the expressions. yix, t) = 92(3, 1) = A sin(kr -wt) A sin(kr + wt) Where k is the wave number, related to the wavelength as k = 2/1, and w is the angular frequency, related to the frequency by w = 2xf. If these two waves interfere with each other and have the same amplitude and frequency, we can add them using the principle of superposition Ystanding (x, t) = (x, t) + y2(x, t) = A (sin(kr - wt) + sin(kx + wt)] = 2A sin(kx) cos(wt) (4) We call the result a "standing wave". This standing wave does not appear to travel one direction or the other and has the presence of "nodes" (points on the string which do not move at all). This interference between two waves traveling in opposite directions is exactly what happens if you send two wave pulses down a string which is fixed at one end. Waves will reflect off of the fixed end, travel back toward the source and interfere with the waves which have yet to hit the fixed end.

Answer 1

Given - Standing wave can y (x, t) - 2 A Sinky Cusat (4) standing 4. Alle standing L, t)= 0 at any time Som 4 You (Lyt) = 2A Sin(KL) Conkot) 0 = 2 A SiNKL) Coswt) - Sin(KL)=0 for any time t - K L = nr where in telong to . Integers To when sin o=07 - nr :. Ik lang 12=not required UŽ om Condition and egn 5. Ans. k=206 from 6 and 16 I = nt (257 6 (x - 24 n

6. Ans. from ea when n-1 T 6 tant DO When n=2 = 2 2 2 1/2 L = When na3 - 3 L-})

t = v I velocity of wave to ý th frequency] fone He"®? 8. Ans. Speed of wave 10 T Tension Tinistring where l = linear mars Density of String from @ and @ tu = ü *10 g An. from free body diagram of mass M. IEW -mg +13 V W = mg where g = Acceleration due to gravity W = Weight of mass m.

10) Ans. - from 12 and 1 n [ Mg Required equation Checking units of right hand side 1 kg m5² = m v kg ml I.. Whit of length L = m M 11 mass m = kg 11 accelera g = ms2 tione M - kg the mass M = kg me per unit length m ms = 5 or hertz which is unit of frequency (f) of left hand side. Ans. from ean (12) by = 7 J

Now Plot graph on X Y plane as to along yanis and IT along X anis Hence Y = mx ط عمهطيل slope alu - on comparing slope (m ) OLJM