The speed of sound can be determined using the formula:
v = fλ
where v is the speed of sound, f is the frequency of the tuning fork and λ is the wavelength of the sound wave.
The wavelength of the sound wave can be calculated using the formula:
λ = 4L/n
where L is the length of the tube and n is the harmonic number.
From the given data, we have two tubes with lengths 30.0 cm and 98.0 cm that produce extra loud sounds for a tuning fork with a frequency of 256 Hz. The length of the tube with one closed end and one open end is equal to one-fourth of the wavelength of the sound wave produced by the tuning fork. Therefore, we can calculate the wavelength as follows:
λ = 4L/n
For L = 30.0 cm and n = 1,
λ1 = 4(30.0 cm)/1 = 120.0 cm
For L = 98.0 cm and n = 1,
λ2 = 4(98.0 cm)/1 = 392.0 cm
Since both tubes produce extra loud sounds for a tuning fork with a frequency of 256 Hz, we can assume that this frequency corresponds to the fundamental frequency (n=1). Therefore, we can calculate the speed of sound as follows:
v = fλ
v = (256 Hz)(120.0 cm) = 30720 cm/s
v = (256 Hz)(392.0 cm) = 100352 cm/s
Therefore, according to this data, the speed of sound is approximately 30720 cm/s or 100352 cm/s depending on which tube was used.