Source: Apple/Beats

When Apple (AAPL -0.81%) acquired Beats, it picked up more than a quality headphone company, streaming music service, and the knowledge of music legends Dr. Dre and Jimmy Iovine. Apple appears to have also acquired another competitor: Bose. If Bose's newest job offer is any indication, the company plans to challenge Apple on a new front. 

Last week, the company posted a job listing for a Senior User Experience Designer: Cloud Music Services. The job description is more succinct: "We are seeking an expert Experience Designer to lead design and prototyping of our next generation streaming music platform and ecosystem of products." And with that, it appears the company is ratcheting up its battle against Beats and its current owner -- former Bose ally -- Apple.

Apple's inherited competition
When Apple paid $3 billion for Beats earlier this year, it turned a longtime ally into a competitor of sorts. For years, Bose had significant market share in the premium headphones market with its QuietComfort Noise Cancelling line and other offerings which paired well with Apple, a company that CEO Tim Cook says has music in its DNA. But more recently, an opportunistic Beats was able to quickly grow and steal market share from Bose by targeting a younger audience and playing up its perceived "coolness factor." The company quickly exploded, growing revenue in just five years to an estimated $1.5 billion in 2013.

In July, following the merger announcement, Bose sued Beats for patent infringement related to its noise cancellation technology. In an aggressive move, Bose sought an injunction to ban any Beats products with the technology from being sold in the United States. Although the two companies settled the dispute -- the terms were undisclosed -- competition between them only increased going forward.

"Official Sound of the NFL" and removal from Apple.com
The rivalry continued as Bose inked a new deal with the NFL. By becoming the "official sound of the NFL," Bose drew the ire of some NFL players when it was announced that they could no longer be seen wearing Beats headphones during TV interviews and in the locker rooms. The ban remains in place until 90 minutes after a game has ended. The NFL enforced the policy early, fining San Francisco quarterback Colin Kaepernick $10,000 for wearing Beats headphones during an interview. 

Although Beats founder Jimmy Iovine responded positively to the publicity from the NFL's strong-arm tactics,  Apple was not quite so enthused -- the company inexplicably pulled Bose accessories from both retail operations and its online store in October. After a short hiatus, Bose products are now back on Apple.com.

Bose needs a win more than Apple
While very little is known about Bose's financials (it's a privately held company), Forbes estimates its revenue at approximately $3 billion. With the aforementioned $1.5 billion of revenue for Beats, Bose is a larger entity overall, but it also produces a wider range of products.

According to a Fast Company article, Beats has managed to grow revenue at an estimated 62% annualized since 2011 -- a staggering pace. The article also included data from NPD which shows Beats as the new market leader in the $100-plus headphone industry with a 60% market share. Bose may be the bigger player when compared head-to-head its younger rival, but the company must now face a Beats with the full faith and support of Apple (a retail giant with $183 billion of revenue).

On the streaming radio front, Apple has its own iTunes Radio and also the Beats Music brand with Beats Electronic purchase, but neither streaming service is key to Apple's top line. Overall, Apple appears more concerned with improving the user experience and leveraging streaming music to bolster iTunes digital downloads than using the service as a revenue driver in its own right. And that makes sense, considering Apple makes significantly more money through hardware than content.

In the end, Bose could experience streaming-music success, but this should have little -- if any -- impact on Apple's business.