1. ans: 230 Hz; use f = v/l.

2. ans: 10.0 m/s; use v = f*l.

3. ans: 1.73; v = sqrt(T/m), f = v/l (l remains unchanged).

4. ans: 50 grams; v = f*l = f*2L, m = T/v², m = m*L.

5. ans: 1500 Hz; 1st overtone = 2f, 2nd = 3f, etc.

6. ans: 37.78 m/s; to solve with high accuracy one needs two equations for two unknowns, 1000 = f*340/(340+v) and 800 = f*340/(340-v), where f = source frequency and v = train speed. One can estimate by assuming f = 900 and solving either equation for v.

7. ans: 1.0; v_new = sqrt(2T/.5m) = 2v_old. f_new = v_new/(2L_new) = 2v_old/(4L_old).

8. ans: 1020 m; d = (v.sound)*t; assume light travel instantaneous.

9. ans: 51.5 kHz; the wall "hears" and reflects 50*340/(340-5). The bat flies into this reflected wave and hears 50*(340+5)/(340-5).