A 280 Hz sound wave is directed into one end of the trombone slide seen in FIGURE P17.55. A microphone is placed at the other end to record the intensity of sound waves that are transmitted through the tube. The straight sides of the slide are 80 cm in length and 10 cm apart with a semicircular bend at the end. For what slide extensions s will the microphone detect a maximum of sound intensity?

Verified step by step guidance

1. Calculate the total length of the trombone slide, which includes the straight sections and the semicircular bend. The straight sections are each 80 cm long, and the semicircular bend has a diameter of 10 cm, giving it a length of 10π cm.
2. Determine the wavelength of the sound wave using the formula λ = v/f, where v is the speed of sound (approximately 343 m/s) and f is the frequency (280 Hz).
3. Identify the condition for constructive interference, which occurs when the path difference is an integer multiple of the wavelength (nλ).
4. Set up the equation for the total length of the trombone slide plus the variable extension s to be equal to an integer multiple of the wavelength: 2(80 cm) + 10π cm + s = nλ.
5. Solve for the variable extension s that satisfies the condition for constructive interference, ensuring that the microphone detects a maximum of sound intensity.