Recording streaming audio

You may find yourself in need of recording audio using your desktop, laptop, or other mobile device. Below sections will introduce detailed steps of each device respectively.

Mac
All Macs (laptops and desktops) come with a built-in microphone.

1. Go to your Applications folder.
2. Open QuickTime Player.
3. Click File>New Audio Recording.
4. Click the red record button to begin recording.
5. Click the black stop button to stop recording.
6. Go to File>Save As to save your file to your desired location.

PC
All laptops and all-in-one computers have a built-in microphone. For users that have a monitor configuration, you may use some software to record internal audio, such as Leawo Music Recorder

1. Install and download Leawo Music Recorder on your computer.
2. Launch it and prepare what you want to record.
3. Click the start button and play the source audio at the same time.
4. Click the button again and save the recording in MP3 or WAV format.

Web
There are many web-based voice recording tools, such as Online Voice Recorder: Record Voice from the Microphone

1. Go to Record Voice from the Microphone.
2. If prompted by your browser, click Allow Microphone Access. You may also click on the Settings button to configure your microphone.
3. Click the red record button to begin recording.
4. Click the record button to end recording.
5. Click Save to download your recording.

iPhone
Open the Voice Memos app (all iPhones have this app, and it can't be deleted)

1. Press the red record button to begin recording.
2. Press the red stop button to stop recording.
3. Tap Done.
4. Type a name for your recording.
5. Press Save.
6. Tap your recording.
7. Press the share icon and email or AirDrop the file to another computer or device.

Android
Each Android device is different, and different carriers may load different apps on the device. Because of this, there is no standard voice recorder app for Android like there is for iOS. Your device may have an app installed already (look for apps labeled "Recorder," "Voice Recorder," "Memo," "Notes," etc.), or you may have to download one from the Google Play store (search for "Voice Recorder" and find an app that meets your needs). Because the apps may vary, the instructions below are more of a guide.

1. Locate or download a recorder app on your phone and click to open.
2. Press the Record button to begin recording.
3. Press the Stop button to end recording.
4. Tap your recording to share.

Source: How to Record Audio on Computer or Your Phone?

It's too difficult to record audio with Adobe audition. So I recommend you to use Leawo music Recorder. Leawo Music Recorder could well play the role of an online audio recorder, helping you easily record music from the internet and save into MP3 or WAV format as you like for multiple audio players. This online audio recorder is an easy to use but practical audio recording app that could get music off the internet for free for you. It could record online audio file from YouTube, Pandora, Last.FM, Napster, Spotify, GUBA, NPC, MySpace, etc. The other function that makes this online streaming audio recorder program top others is that it could automatically download and add song tags to recorded audio files, including song artist, song album, album artwork, song name, etc.
For Mac users, the Leawo Music Recorder for Mac could serve you well. Check the below steps to know how to easily record audio online and get music off the internet for free.

Want to lean simple step-by-step tuturial guide? Check: https://www.leawo.org/tutorial/how-to-record-audio-from-the-internet.html

I know a tool named wondershare streaming audio recorder.

According to the technology of Virtual sound card, it can record any sound signal through your sound card. And the sound quality is good.

As we know, it can also record sound from online streaming music, radio station, Microphone, telephone,etc.

Find a step by step guide and tips for your reference.
http://www.flash-on-tv.com/article/record-online-music-guide.html

You can have a try.

You would have to set adobe up to record from the wave device. But I cannot recommend or tell you how to go about this due to the fact streaming audio is 99% of the time copywritten material.