An explosion occurs at the end of a pier. The sound reaches the other end of the pier by traveling through three media: air, fresh water, and a slender metal handrail. The speeds of sound in air, water, and the handrail are 339, 1480, and 5060 m/s, respectively. The sound travels a distance of 141 m in each medium.

(a) After the first sound arrives, how much later does the second sound arrive?
(b) After the first sound arrives, how much later does the third sound arrive?

Based on the speed of sound in each medium ([tex]s_{air}=339m/s, s_{water}=1480m/s, s_{metal}=5060m/s[/tex]) the sound will first arrive via the metal handrail, then the water and lastly the air.

[tex]t=\frac{d}{s}[/tex] , where 't' is time, 'd' is distance and 's' is speed

[tex]t_{metal}=\frac{d}{s_{metal}}[/tex]

[tex]t_{metal}=\frac{141}{5060}[/tex]

[tex]t_{metal}=0.0279s[/tex]

[tex]t_{water}=\frac{d}{s_{water}}[/tex]

[tex]t_{water}=\frac{141}{1480}[/tex]

[tex]t_{water}=0.0953s[/tex]

[tex]t_{air}=\frac{d}{s_{air}}[/tex]

[tex]t_{air}=\frac{141}{339}[/tex]

[tex]t_{air}=0.4159s[/tex]

a) Time difference between the first and second sound

[tex]t_{water}-t_{metal}[/tex]

[tex]0.0953-0.0279[/tex]

[tex]0.0674s[/tex]

b) Time difference between the first and third sound

[tex]t_{air}-t_{metal}[/tex]

[tex]0.4159-0.0279[/tex]

[tex]0.3880s[/tex]